P8_code_reponse

library(dataQualityR) #for data cleaning
library(e1071) #SVM Training & Testing Models
library(mice) #deal with missing data
library(corrplot) #plot for correlation matrix
library(ggplot2) #visualization and plots
library(ggpubr) #customizing ggplot2
library(scales) #graphical scales map data to aesthetics
library(caret) #deal with Classification And REgression Training CART
library(dplyr) #data manipulation: filter and arrange
library(tidyverse) #data manipulation
library(sf) #plot mapping
library(gganimate) #static visualization
library(MASS) #deal with data set
library(VIM) #tools for the visualization of missing or imputed values
library(glmnet) #Lasso and Elastic-Net Regularization

Outline:

1. Introduction - Business Context
2. Data Preparation 2.1. Data collection 2.2. Data Cleaning 2.3. Correlation Analysis
3. Exploratory Data Analysis - EDA
4. Modeling
5. Evaluation

1. Introduction

Ce projet vise à déterminer les caractéristiques qui sont les meilleurs indicateurs de la qualité du vin rouge et à générer un aperçu de chacun de ces facteurs pour la qualité du vin rouge de notre modèle. Par la suite, ce modèle pourra servir les entreprises du secteur à prédire la qualité de leur vin.

2. Data Preparation

• Fixed Acidity: sont des acides non volatils qui ne s’évaporent pas facilement.
• Volatile Acidity: sont des taux élevés d’acide acétique dans le vin, ce qui donne un goût de vinaigre désagréable
• Citric Acid: agit comme un conservateur pour augmenter l’acidité. En petites quantités, il ajoute de la fraîcheur et de la saveur aux vins.
• Residual Sugar: est la quantité de sucre restant après l’arrêt de la fermentation. L’essentiel est d’obtenir un équilibre parfait entre la douceur et l’acidité. Il est important de noter que les vins de plus de 45 g/litre sont sucrés.
• Chlorides: la quantité de sel dans le vin
• Free Sulfur Dioxide: il empêche la croissance microbienne et l’oxydation du vin
• Total Sulfur Dioxide: est la quantité de formes libres + liées de SO2
• Density: les vins plus doux ont une densité plus élevée
• pH: décrit le niveau d’acidité sur une échelle de 0 à 14. La plupart des vins se situent toujours entre 3 et 4 sur l’échelle du pH.
• Alcohol: disponible en petites quantités dans les vins rend les buveurs sociables
• Sulphates: un additif pour le vin qui contribue aux niveaux de SO2 et agit comme antimicrobien et antioxydant
• Quality: qui est la variable de sortie/prédicteur ## 2.1. Data collection

2.2. Data cleaning

• Data reading

df<-read.csv("winequality-red.csv")
dim(df)

## [1] 1599   12

• Data overview

str(df)

## 'data.frame':    1599 obs. of  12 variables:
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

summary(df)

##  fixed.acidity   volatile.acidity  citric.acid    residual.sugar  
##  Min.   : 4.60   Min.   :0.1200   Min.   :0.000   Min.   : 0.900  
##  1st Qu.: 7.10   1st Qu.:0.3900   1st Qu.:0.090   1st Qu.: 1.900  
##  Median : 7.90   Median :0.5200   Median :0.260   Median : 2.200  
##  Mean   : 8.32   Mean   :0.5278   Mean   :0.271   Mean   : 2.539  
##  3rd Qu.: 9.20   3rd Qu.:0.6400   3rd Qu.:0.420   3rd Qu.: 2.600  
##  Max.   :15.90   Max.   :1.5800   Max.   :1.000   Max.   :15.500  
##    chlorides       free.sulfur.dioxide total.sulfur.dioxide    density      
##  Min.   :0.01200   Min.   : 1.00       Min.   :  6.00       Min.   :0.9901  
##  1st Qu.:0.07000   1st Qu.: 7.00       1st Qu.: 22.00       1st Qu.:0.9956  
##  Median :0.07900   Median :14.00       Median : 38.00       Median :0.9968  
##  Mean   :0.08747   Mean   :15.87       Mean   : 46.47       Mean   :0.9967  
##  3rd Qu.:0.09000   3rd Qu.:21.00       3rd Qu.: 62.00       3rd Qu.:0.9978  
##  Max.   :0.61100   Max.   :72.00       Max.   :289.00       Max.   :1.0037  
##        pH          sulphates         alcohol         quality     
##  Min.   :2.740   Min.   :0.3300   Min.   : 8.40   Min.   :3.000  
##  1st Qu.:3.210   1st Qu.:0.5500   1st Qu.: 9.50   1st Qu.:5.000  
##  Median :3.310   Median :0.6200   Median :10.20   Median :6.000  
##  Mean   :3.311   Mean   :0.6581   Mean   :10.42   Mean   :5.636  
##  3rd Qu.:3.400   3rd Qu.:0.7300   3rd Qu.:11.10   3rd Qu.:6.000  
##  Max.   :4.010   Max.   :2.0000   Max.   :14.90   Max.   :8.000

• data report pour cat et num

num.file <- paste(getwd(), "/dqames_num.csv", sep= "")
cat.file <- paste(getwd(), "/dqames_cat.csv", sep= "")
checkDataQuality(data= df, out.file.num= num.file, out.file.cat= cat.file)

## Check for numeric variables completed // Results saved to disk // Time difference of 0.02191997 secs
##  // Time difference of 0.000003099442 secs

• Vérification des données manquantes

aggr_plot <- aggr(df, col=c('navyblue','red'), numbers=TRUE, sortVars=TRUE, labels=names(df), cex.axis=.7, gap=3, ylab=c("Histogram of missing data","Pattern"))

## 
##  Variables sorted by number of missings: 
##              Variable Count
##         fixed.acidity     0
##      volatile.acidity     0
##           citric.acid     0
##        residual.sugar     0
##             chlorides     0
##   free.sulfur.dioxide     0
##  total.sulfur.dioxide     0
##               density     0
##                    pH     0
##             sulphates     0
##               alcohol     0
##               quality     0

2.3. Correlation analysis

• Matrice de corrélation

set.seed(123)
library(dplyr)
library(tidyr)

cor(df) %>%
  as.data.frame() %>%
  mutate(var1 = rownames(.)) %>%
  gather(var2, value, -var1) %>%
  arrange(desc(value)) %>%
  group_by(value) %>%
  filter(row_number()==1)

## # A tibble: 67 × 3
## # Groups:   value [67]
##    var1                 var2                value
##    <chr>                <chr>               <dbl>
##  1 fixed.acidity        fixed.acidity       1    
##  2 citric.acid          fixed.acidity       0.672
##  3 density              fixed.acidity       0.668
##  4 total.sulfur.dioxide free.sulfur.dioxide 0.668
##  5 quality              alcohol             0.476
##  6 sulphates            chlorides           0.371
##  7 density              citric.acid         0.365
##  8 density              residual.sugar      0.355
##  9 sulphates            citric.acid         0.313
## 10 quality              sulphates           0.251
## # … with 57 more rows

dfcor <- cor(df)
corrplot(dfcor, method = "color", addCoef.col = "black",number.cex = .6,
         tl.col = "black", tl.srt = 90, diag = FALSE)

• Construciton des corrélation atts avec la variable Quality

dfcor <- cor(df)
quality_cor <- dfcor[,12]
absoutcome_cor <- abs(quality_cor)
head(absoutcome_cor[order(absoutcome_cor, decreasing = TRUE)],12)

##              quality              alcohol     volatile.acidity 
##           1.00000000           0.47616632           0.39055778 
##            sulphates          citric.acid total.sulfur.dioxide 
##           0.25139708           0.22637251           0.18510029 
##              density            chlorides        fixed.acidity 
##           0.17491923           0.12890656           0.12405165 
##                   pH  free.sulfur.dioxide       residual.sugar 
##           0.05773139           0.05065606           0.01373164

3. Exploratory Data Analysis - EDA

3.1. Overall Quality

q1 <- ggplot(df, aes(quality))+ 
  geom_histogram() + 
  labs(title = "Histogram of quality") + 
  theme(plot.title=element_text(hjust=0.5)) +
  geom_vline(aes(xintercept=mean(quality)), color="blue", linetype="dashed", size=1) +
  geom_text(aes(x=5.6, label="Mean Value", y=400), colour="red", angle=90, vjust = 1.2, text=element_text(size=11))
q1

q2 <- ggplot(df, aes(sample=quality)) +
  stat_qq(color="dodgerblue4") + 
  stat_qq_line(color="red") +
  scale_y_continuous(labels=function(y){y/10^6}) +
  labs(title="QQ Plot for quality", y="Ordered Values") +
  theme(plot.title=element_text(hjust=0.5))
q2

3.2. graphs des distributions marginales de quantités numériques clés

p1 <- ggplot(df, aes(x=fixed.acidity)) + 
  geom_density()
p1 + geom_vline(aes(xintercept=mean(fixed.acidity)),
            color="blue", linetype="dashed", size=1)

p2 <- ggplot(df, aes(x=volatile.acidity)) + 
  geom_density()
p2 + geom_vline(aes(xintercept=mean(volatile.acidity)),
            color="blue", linetype="dashed", size=1)

p3 <- ggplot(df, aes(x=citric.acid)) + 
  geom_density()
p3 + geom_vline(aes(xintercept=mean(citric.acid)),
            color="blue", linetype="dashed", size=1)

p4 <- ggplot(df, aes(x=residual.sugar)) + 
  geom_density()
p4 + geom_vline(aes(xintercept=mean(residual.sugar)),
            color="blue", linetype="dashed", size=1)

p5 <- ggplot(df, aes(x=chlorides)) + 
  geom_density()
p5 + geom_vline(aes(xintercept=mean(chlorides)),
            color="blue", linetype="dashed", size=1)

p6 <- ggplot(df, aes(x=free.sulfur.dioxide)) + 
  geom_density()
p6 + geom_vline(aes(xintercept=mean(free.sulfur.dioxide)),
            color="blue", linetype="dashed", size=1)

p7 <- ggplot(df, aes(x=total.sulfur.dioxide)) + 
  geom_density()
p7 + geom_vline(aes(xintercept=mean(total.sulfur.dioxide)),
            color="blue", linetype="dashed", size=1)

p8 <- ggplot(df, aes(x=density)) + 
  geom_density()
p8 + geom_vline(aes(xintercept=mean(density)),
            color="blue", linetype="dashed", size=1)

p9 <- ggplot(df, aes(x=pH)) + 
  geom_density()
p9 + geom_vline(aes(xintercept=mean(pH)),
            color="blue", linetype="dashed", size=1)

p10 <- ggplot(df, aes(x=sulphates)) + 
  geom_density()
p10 + geom_vline(aes(xintercept=mean(sulphates)),
            color="blue", linetype="dashed", size=1)

p11 <- ggplot(df, aes(x=alcohol)) + 
  geom_density()
p11 + geom_vline(aes(xintercept=mean(alcohol)),
            color="blue", linetype="dashed", size=1)

ggarrange(p1, p2, p3, p4, nrow = 2, ncol =2)

ggarrange(p5, p6, p7, p8, nrow = 2, ncol =2)

ggarrange(p9, p10, p11, nrow = 2, ncol =2)

b1 <- boxplot(df$fixed.acidity, col="slategray2", pch=19)

b2 <- boxplot(df$volatile.acidity, col="slategray2", pch=19)

b3 <- boxplot(df$citric.acid, col="slategray2", pch=19)

b4 <- boxplot(df$residual.sugar, col="slategray2", pch=19)

b5 <- boxplot(df$chlorides, col="slategray2", pch=19)

b6 <- boxplot(df$free.sulfur.dioxide, col="slategray2", pch=19)

b7 <- boxplot(df$total.sulfur.dioxide, col="slategray2", pch=19)

b8 <- boxplot(df$density, col="slategray2", pch=19)

b9 <- boxplot(df$pH, col="slategray2", pch=19)

b10 <- boxplot(df$sulphates, col="slategray2", pch=19)

b11 <- boxplot(df$alcohol, col="slategray2", pch=19)

3.3. Contrôle de la qualité par rapport à des variables numériques

g1 <- ggplot(df, aes(factor(quality), fixed.acidity, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "fixed.acidity", title = "Boxplot of Quality vs. fixed.acidity") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g1

g2 <- ggplot(df, aes(factor(quality), volatile.acidity, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "volatile.acidity", title = "Boxplot of Quality vs. volatile.acidity") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g2

g3 <- ggplot(df, aes(factor(quality), citric.acid, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "citric.acid", title = "Boxplot of Quality vs. citric.acid") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g3

g4 <- ggplot(df, aes(factor(quality), residual.sugar, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "residual.sugar", title = "Boxplot of Quality vs. residual.sugar") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g4

ggarrange(g1, g2, g3, g4, nrow = 2, ncol =2)

# Il semble qu'il y ait une relation positive entre citric acid et quality.
# Il semble qu'il y ait une relation négative entre volatile acidity et quality.

g5 <- ggplot(df, aes(factor(quality), chlorides, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "Quality", y = "chlorides", title = "Boxplot of Quality vs. chlorides") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g5

g6 <- ggplot(df, aes(factor(quality), free.sulfur.dioxide, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "free.sulfur.dioxide", title = "Boxplot of quality vs. free.sulfur.dioxide") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g6

g7 <- ggplot(df, aes(factor(quality), total.sulfur.dioxide, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "total.sulfur.dioxide", title = "Boxplot of quality vs. total.sulfur.dioxide") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g7

g8 <- ggplot(df, aes(factor(quality), density, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "density", title = "Boxplot of quality vs. density") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g8

ggarrange(g5, g6, g7, g8, nrow = 2, ncol =2)

# Il semble qu'il y ait une relation négative entre density acid et quality.

g9 <- ggplot(df, aes(factor(quality), pH, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "pH", title = "Boxplot of Quality vs. pH") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g9

g10 <- ggplot(df, aes(factor(quality), sulphates, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "sulphates", title = "Boxplot of quality vs. sulphates") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g10

g11 <- ggplot(df, aes(factor(quality), alcohol, fill=factor(quality))) + 
  geom_boxplot() +
  labs(x = "quality", y = "alcohol", title = "Boxplot of quality vs. alcohol") + 
  theme(legend.position = 'none', plot.title = element_text(size = 9, hjust=0.5))
g11

ggarrange(g9, g10, g11, nrow = 2, ncol =2)

# Il semble qu'il y ait une relation positive entre alcohol et quality.
# Il semble qu'il y ait une relation positive entre sulphates et quality. 

3.3. Inspection de la relation entre les variables numériques

s1 <- ggplot(df, aes(x=fixed.acidity, y=citric.acid)) +
  geom_point(color="dodgerblue4",size=0.7) + 
  labs(title="fixed.acidity vs. citric.acid") +
  geom_smooth(formula=y~x,method=lm, color="red") +
  theme(plot.title=element_text(hjust=0.5))
s1

s2 <- ggplot(df, aes(x=fixed.acidity, y=density)) +
  geom_point(color="dodgerblue4",size=0.7) + 
  labs(title="fixed.acidity vs. density") +
  geom_smooth(formula=y~x,method=lm, color="red") +
  theme(plot.title=element_text(hjust=0.5))
s2

s3 <- ggplot(df, aes(x=free.sulfur.dioxide, y=total.sulfur.dioxide)) +
  geom_point(color="dodgerblue4",size=0.7) + 
  labs(title="free.sulfur.dioxide vs. total.sulfur.dioxide") +
  geom_smooth(formula=y~x,method=lm, color="red") +
  theme(plot.title=element_text(hjust=0.5))
s3

s4 <- ggplot(df, aes(x=fixed.acidity, y=pH)) +
  geom_point(color="dodgerblue4",size=0.7) + 
  labs(title="fixed.acidity vs. pH") +
  geom_smooth(formula=y~x,method=lm, color="red") +
  theme(plot.title=element_text(hjust=0.5))
s4

ggarrange(s1, s2, s3, s4, nrow = 2, ncol =2)

# Il semble qu'il y ait une relation positive entre fixed.acidity et citric.acid
# Il semble qu'il y ait une relation positive entre fixed.acidity et density
# Il semble qu'il y ait une relation positive entre free.sulfur.dioxide et total.sulfur.dioxide
# Il semble qu'il y ait une relation negative entre fixed.acidity et pH

3.4. Inspection 3D

i1<- ggplot(df, aes(x=factor(round(alcohol)), y=citric.acid)) + 
  geom_boxplot(aes(colour = factor(quality))) +
  labs(title="Alcohol + Citric.Acid vs. Quality") + 
  theme(plot.title=element_text(hjust=0.5))
i1

i2 <- ggplot(df, aes(x=factor(round(alcohol)), y=volatile.acidity)) + 
  geom_boxplot(aes(colour = factor(quality))) +
  labs(title="Alcohol + Volatile.Acidity vs. Quality") + 
  theme(plot.title=element_text(hjust=0.5))
i2

i3 <- ggplot(df, aes(x=factor(round(alcohol)), y=chlorides)) + 
  geom_boxplot(aes(colour = factor(quality))) +
  labs(title="Alcohol + Chlorides vs. Quality") + ylim(0, 0.3)
  theme(plot.title=element_text(hjust=0.5))

## List of 1
##  $ plot.title:List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : num 0.5
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi FALSE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  - attr(*, "class")= chr [1:2] "theme" "gg"
##  - attr(*, "complete")= logi FALSE
##  - attr(*, "validate")= logi TRUE

i3

4. Modeling

4.1. Modélisation avec les 5 principales variables

4.1. Modèle 1 avec top 5 plus haute corrélation avec TotalIncidents

lm0 <- lm(quality ~ alcohol + volatile.acidity +  sulphates + citric.acid + total.sulfur.dioxide, data = df)
summary(lm0)

## 
## Call:
## lm(formula = quality ~ alcohol + volatile.acidity + sulphates + 
##     citric.acid + total.sulfur.dioxide, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.72463 -0.38380 -0.06689  0.44606  2.14550 
## 
## Coefficients:
##                        Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)           2.8431068  0.2050732  13.864 < 0.0000000000000002 ***
## alcohol               0.2953419  0.0160375  18.416 < 0.0000000000000002 ***
## volatile.acidity     -1.2223102  0.1124774 -10.867 < 0.0000000000000002 ***
## sulphates             0.7207881  0.1027039   7.018     0.00000000000332 ***
## citric.acid          -0.0427246  0.1035810  -0.412                 0.68    
## total.sulfur.dioxide -0.0022182  0.0005126  -4.327     0.00001602753699 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6552 on 1593 degrees of freedom
## Multiple R-squared:  0.3439, Adjusted R-squared:  0.3418 
## F-statistic:   167 on 5 and 1593 DF,  p-value: < 0.00000000000000022

lm1 <- lm(quality ~ alcohol + volatile.acidity +  sulphates + total.sulfur.dioxide, data = df)
summary(lm1)

## 
## Call:
## lm(formula = quality ~ alcohol + volatile.acidity + sulphates + 
##     total.sulfur.dioxide, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.72716 -0.38486 -0.06503  0.44980  2.13257 
## 
## Coefficients:
##                        Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)           2.8258128  0.2006892  14.081 < 0.0000000000000002 ***
## alcohol               0.2953105  0.0160331  18.419 < 0.0000000000000002 ***
## volatile.acidity     -1.1985632  0.0966011 -12.407 < 0.0000000000000002 ***
## sulphates             0.7121396  0.1005146   7.085     0.00000000000208 ***
## total.sulfur.dioxide -0.0022354  0.0005108  -4.376     0.00001284518270 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.655 on 1594 degrees of freedom
## Multiple R-squared:  0.3438, Adjusted R-squared:  0.3421 
## F-statistic: 208.8 on 4 and 1594 DF,  p-value: < 0.00000000000000022

# Define training control
set.seed(123) 
train.control <- trainControl(method = "cv", number = 10) #cv Cross-Validation
# Train the model
model1 <- train(quality ~ alcohol + volatile.acidity +  sulphates + total.sulfur.dioxide, data = df, method = "lm", trControl = train.control)
# Summarize the results
summary(model1)

## 
## Call:
## lm(formula = .outcome ~ ., data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.72716 -0.38486 -0.06503  0.44980  2.13257 
## 
## Coefficients:
##                        Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)           2.8258128  0.2006892  14.081 < 0.0000000000000002 ***
## alcohol               0.2953105  0.0160331  18.419 < 0.0000000000000002 ***
## volatile.acidity     -1.1985632  0.0966011 -12.407 < 0.0000000000000002 ***
## sulphates             0.7121396  0.1005146   7.085     0.00000000000208 ***
## total.sulfur.dioxide -0.0022354  0.0005108  -4.376     0.00001284518270 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.655 on 1594 degrees of freedom
## Multiple R-squared:  0.3438, Adjusted R-squared:  0.3421 
## F-statistic: 208.8 on 4 and 1594 DF,  p-value: < 0.00000000000000022

print(model1)

## Linear Regression 
## 
## 1599 samples
##    4 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1439, 1439, 1438, 1439, 1439, 1440, ... 
## Resampling results:
## 
##   RMSE       Rsquared   MAE      
##   0.6560876  0.3429191  0.5099489
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

4.2. LASSO

library(glmnet)
x <- model.matrix(quality~., df)[,-1]
y <- df$quality
mod <- cv.glmnet(as.matrix(x), y, alpha=1)

as.matrix(coef(mod, mod$lambda.min))

##                                 s1
## (Intercept)           18.731818444
## fixed.acidity          0.020774482
## volatile.acidity      -1.078204434
## citric.acid           -0.164074955
## residual.sugar         0.014319348
## chlorides             -1.867641097
## free.sulfur.dioxide    0.004233406
## total.sulfur.dioxide  -0.003228361
## density              -14.593604735
## pH                    -0.422494118
## sulphates              0.906073568
## alcohol                0.278563263

as.matrix(coef(mod, mod$lambda.1se))

##                                 s1
## (Intercept)           3.1453849170
## fixed.acidity         0.0018155594
## volatile.acidity     -1.0221755767
## citric.acid           0.0000000000
## residual.sugar        0.0000000000
## chlorides            -0.2350727376
## free.sulfur.dioxide   0.0000000000
## total.sulfur.dioxide -0.0009327824
## density               0.0000000000
## pH                    0.0000000000
## sulphates             0.4961365592
## alcohol               0.2640733125

CF <- as.matrix(coef(mod, mod$lambda.1se))
CF[CF!=0,]

##          (Intercept)        fixed.acidity     volatile.acidity 
##         3.1453849170         0.0018155594        -1.0221755767 
##            chlorides total.sulfur.dioxide            sulphates 
##        -0.2350727376        -0.0009327824         0.4961365592 
##              alcohol 
##         0.2640733125

lm2 <- lm(quality ~ fixed.acidity + volatile.acidity + chlorides + total.sulfur.dioxide + sulphates + alcohol, data=df)
summary(lm2)

## 
## Call:
## lm(formula = quality ~ fixed.acidity + volatile.acidity + chlorides + 
##     total.sulfur.dioxide + sulphates + alcohol, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.70812 -0.37181 -0.06238  0.45933  1.99472 
## 
## Coefficients:
##                        Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)           2.7365412  0.2325021  11.770 < 0.0000000000000002 ***
## fixed.acidity         0.0236576  0.0099187   2.385               0.0172 *  
## volatile.acidity     -1.0856214  0.0996323 -10.896 < 0.0000000000000002 ***
## chlorides            -1.7376885  0.3913566  -4.440  0.00000960779597327 ***
## total.sulfur.dioxide -0.0021460  0.0005121  -4.191  0.00002933553690691 ***
## sulphates             0.8846921  0.1108310   7.982  0.00000000000000272 ***
## alcohol               0.2825603  0.0166180  17.003 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6504 on 1592 degrees of freedom
## Multiple R-squared:  0.3538, Adjusted R-squared:  0.3514 
## F-statistic: 145.3 on 6 and 1592 DF,  p-value: < 0.00000000000000022

# Define training control
set.seed(123) 
train.control <- trainControl(method = "cv", number = 10) #cv Cross-Validation
# Train  model
model2<- train(quality ~ fixed.acidity + volatile.acidity + chlorides + total.sulfur.dioxide + sulphates + alcohol,data = df, method = "lm",
               trControl = train.control)
#results
summary(model2)

## 
## Call:
## lm(formula = .outcome ~ ., data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.70812 -0.37181 -0.06238  0.45933  1.99472 
## 
## Coefficients:
##                        Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)           2.7365412  0.2325021  11.770 < 0.0000000000000002 ***
## fixed.acidity         0.0236576  0.0099187   2.385               0.0172 *  
## volatile.acidity     -1.0856214  0.0996323 -10.896 < 0.0000000000000002 ***
## chlorides            -1.7376885  0.3913566  -4.440  0.00000960779597327 ***
## total.sulfur.dioxide -0.0021460  0.0005121  -4.191  0.00002933553690691 ***
## sulphates             0.8846921  0.1108310   7.982  0.00000000000000272 ***
## alcohol               0.2825603  0.0166180  17.003 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6504 on 1592 degrees of freedom
## Multiple R-squared:  0.3538, Adjusted R-squared:  0.3514 
## F-statistic: 145.3 on 6 and 1592 DF,  p-value: < 0.00000000000000022

print(model2)

## Linear Regression 
## 
## 1599 samples
##    6 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1439, 1439, 1438, 1439, 1439, 1440, ... 
## Resampling results:
## 
##   RMSE       Rsquared   MAE    
##   0.6525392  0.3496559  0.50698
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

4.3 Random Forest Model 3

library(randomForest)
library(mlbench)
library(caret) # use createDataPartition() function 
set.seed(95014)

# partition 
#Evaluation Sets
set.seed(123)
n = nrow(df)
trainIndex = sample(1:n, size = round(0.7*n), replace=FALSE)

#Crée des dataframe d'entrainemet et des test à partir d'observations
training = df[trainIndex,]
testing = df[-trainIndex,]

model3 <- randomForest(quality ~ ., training, mtry = 3, 
                         importance = TRUE, na.action = na.omit)
print(model3)

## 
## Call:
##  randomForest(formula = quality ~ ., data = training, mtry = 3,      importance = TRUE, na.action = na.omit) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 3
## 
##           Mean of squared residuals: 0.3669176
##                     % Var explained: 46.23

#le graphique de l'erreur en fonction du nombre d'arbres.
plot(model3) 

varImp(model3)

##                       Overall
## fixed.acidity        20.71249
## volatile.acidity     29.63074
## citric.acid          21.53189
## residual.sugar       14.61027
## chlorides            22.20528
## free.sulfur.dioxide  20.00519
## total.sulfur.dioxide 28.35124
## density              28.98152
## pH                   20.88894
## sulphates            44.31574
## alcohol              49.35817

varImpPlot(model3,type=2)

# obtenir MSE à partir du dernier élément dans fit$mse
# qui devrait correspondre à la sortie de l'impression
model3$mse[length(model3$mse)]

## [1] 0.3669176

# prendre la racine carrée pour calculer la RMSE du modèle
sqrt(model3$mse[length(model3$mse)])

## [1] 0.6057372

# illustrons maintenant comment calculer le RMSE sur les données de test par rapport aux données de formation.
predValues <- predict(model3,testing)

# nous pouvons le calculer directement 
sqrt(mean((testing$quality -predValues)^2)) #RMSE

## [1] 0.5506011

mean(abs(testing$quality -predValues)) #MAE

## [1] 0.4104835

Evaluation dataframe

Model <- c("Model 1", "Model 2", "Model 3")
R_squared <- c(0.3479, 0.3546, 0.4850)
RMSE <- c(0.6549, 0.6515, 0.5843)
MAE <- c(0.5092899, 0.5063, 0.4222)
ml <- data.frame(Model, R_squared, RMSE, MAE)

Plot

library(gridExtra)
p1 <- ggplot(ml, aes(Model, RMSE)) + geom_point(aes(colour = factor(Model), size = 4)) + labs(title="RMSE") + theme(plot.title=element_text(hjust=0.5), axis.title.y = element_blank(),axis.title.x = element_blank(), legend.position="none")
p2 <- ggplot(ml, aes(Model, R_squared)) + geom_point(aes(colour = factor(Model), size = 4)) + labs(title="R-Squared") + theme(plot.title=element_text(hjust=0.5), axis.title.y = element_blank(),axis.title.x = element_blank(), legend.position="none")
p3 <- ggplot(ml, aes(Model, MAE)) + geom_point(aes(colour = factor(Model), size = 4)) + labs(title="MAE") + theme(plot.title=element_text(hjust=0.5), axis.title.y = element_blank(),axis.title.x = element_blank(), legend.position="none")
grid.arrange(p2,p1,p3, ncol=3)